Question

[lanhviethoang]

(1)/(1*5)+(1)/(5*9)+(1)/(9*13)+...+(1)/(25*29)
help

Answer 1

[Nguyễn Thị Thương Hoài]

A = \(\dfrac{1}{1.5}\) + \(\dfrac{1}{5.9}\) + \(\dfrac{1}{9.13}\)+ ... + \(\dfrac{1}{25.29}\)

A = \(\dfrac{1}{4}\).(\(\dfrac{4}{1.5}\) + \(\dfrac{4}{5.9}\) + \(\dfrac{4}{9.13}\) + ... + \(\dfrac{4}{25.29}\))

A = \(\dfrac{1}{4}\).(\(\dfrac{1}{1}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{9}\) + \(\dfrac{1}{9}\) - \(\dfrac{1}{13}\) + ... + \(\dfrac{1}{25}\) - \(\dfrac{1}{29}\))

A = \(\dfrac{1}{4}\).(\(\dfrac{1}{1}\) - \(\dfrac{1}{29}\))

A = \(\dfrac{1}{4}\).\(\dfrac{28}{29}\)

A = \(\dfrac{7}{29}\)